Dispensers with draw-back mechanisms are known for dispensing a foamed soap or other material to a user. The draw-back mechanism is used to prevent soap, or other material, from hanging and dripping from the end of the dispensing tube after delivery of the liquid dose. One such dispenser is disclosed in U.S. Pat. No. 7,681,765. Such dispensers may use pumps that dispense foamed liquids. One such pump is disclosed in U.S. Pat. No. 6,536,629.